Visual appearance of industrial surfaces: Haze and gloss

Ingve SimonsenDepartment of Physics,

NTNU, Trondheim, NORWAY

Collaborators

Åge G. Larsen SINTEF Erik Andersen SINTEF Espen Ommundsen Borealis AS Katrin Nord-Varhaug Borealis AS

Motivation

The industry quantifies the visual appearance of optical materials (e.g. haze and gloss)

Materials are categorized according to their visual appearance and functional properties Eg. reflector materials, food wrappings

Science does not seem to “provide” the relevant quantities the industry seems to use haze and gloss for this purpose these quantities are not uniquely defined

(industrial standards)

Plastic materials

Scattering Geometry

2

( ) 0

( ) ( ') '

x

x x W x x

Statistical description: Height distribution Correlation function: W

Power spectrum

ikxg k dxW x e

rms-roughnessa correlation length

q

22

2

s in

( )

m

m m

qc

q qc

Example : Plastic material (LLDPE)

0.041.3

ma m

Question : How can haze and gloss be estimated from the knowledge of surface parameters…?

Question : What about the surface correlations?

Definitions : Haze and gloss

No scientific definition exists Industrial standards

Gloss/haze meters Reference material used Different standards in eg.

America and Europe Wide- and narrow-angle gloss

Haze measures how diffuse a material isGloss measures how speckular it is

=2.5

Definitions : Haze and gloss (cont.)

Simple considerations gives (diffuse field)

Question : But how does haze depend on the height-height correlations along the surface?Ref : Alexander-Katz and Barrera (1998).

Haze (gloss) are defined as the fraction of the reflected/transmitted power that is reflected/transmitted outside(inside) an angular interval about the speckular direction.

2 20( )H k

Approximation to Haze

Phase-perturbation theoretical result

2 20

( )( ) 1 exp ( ) 1 G a qH k k

�

1( )2

q

qG a dq g q

q

Power spectrum factor

Momentum transfer : (k|k) (perpendicular); q (lateral)

Reduced variables : (k|k) and G(a)q

Question :How good is this approximation?

Haze : Numerical results

Comparison to rigorous Monte Carlo simulations:

Haze : Numerical results (cont…)

Gloss : Numerical Results

Experimental results

Measured haze of the plastic material discussed earlier

Estimated from the analytic expression using the measured topography data H1D(0)=0.054

0( 0) 0.189H

1' (0) 0.170DH H

Conclusions

Within the context of phase perturbation theory, we have derived an expression for haze and gloss in terms of reduced variables (k|k) and G(a)q explicitly shows the dependence on the power spectrum g(|k|)

Accessed the accuracy of the approximation good approximation over large regions of parameter space

Thank you for your attention

Scattering results

easured roughness parameters used!Film thickness d=50m

The haze approximation “written out”